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Answer :
(i) For 540 marks, the central angle = \( 360^{ \circ}\)
∴ the central angle for 1 mark = \(\left( \frac { 360 }{ 540 } \right) ^{ \circ }=\left( \frac { 2 }{ 3 } \right) ^{ \circ }\)
∴ the central angle for 105 marks =\( \left( \frac { 2 }{ 3 } \times 105 \right) ^{ \circ }=70^{ \circ }\)
Hence, from the given pie chart, the subject is Hindi.
(ii) Difference between the central angles made by the subject of Mathematics and Hindi= \(90^{\circ} – 70^{\circ} = 20^{\circ}\).
Marks obtained for the central angle of \(360^{\circ}\), = 540
Marks obtained for the central angle of \(1^{\circ}\)=\(\frac { 540 }{ 360 } =\frac { 3 }{ 2 }\)
Marks obtained for the central angle of \(20^{\circ}=\frac { 3 }{ 2 } \times 20=30\)
Hence, the student obtained 30 more marks in Mathematics than Hindi.
(iii) Sum of the central angles made by Social Science and Mathematics =\( 65^{\circ}+ 90^{\circ} = 155^{\circ}\).
And, the sum of the central angles made by Science and Hindi = \(80^{\circ}+ 70^{\circ} = 150^{\circ}\).
Since \(155^{\circ} >150^{\circ}\), therefore, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.